Problem: Solve for $x$ and $y$ using substitution. ${x-3y = 8}$ ${x = -4y+1}$
Answer: Since $x$ has already been solved for, substitute $-4y+1$ for $x$ in the first equation. ${(-4y+1)}{- 3y = 8}$ Simplify and solve for $y$ $-4y+1 - 3y = 8$ $-7y+1 = 8$ $-7y+1{-1} = 8{-1}$ $-7y = 7$ $\dfrac{-7y}{{-7}} = \dfrac{7}{{-7}}$ ${y = -1}$ Now that you know ${y = -1}$ , plug it back into $\thinspace {x = -4y+1}\thinspace$ to find $x$ ${x = -4}{(-1)}{ + 1}$ $x = 4 + 1$ ${x = 5}$ You can also plug ${y = -1}$ into $\thinspace {x-3y = 8}\thinspace$ and get the same answer for $x$ : ${x - 3}{(-1)}{= 8}$ ${x = 5}$